Solving Systems of Nonlinear Equations Using The Cuckoo Optimization Algorithm Mahdi Abdollahi * Aras International Campus. University of Tabriz Department of Computer Sciences m.abdollahi89@ms.tabrizu.ac.ir Shahriar Lotfi University of Tabriz Department of Computer Sciences shahriar lotfi@tabrizu.ac.ir Davoud Abdollahi University of Tabriz Department of Mathematics d abdollahi@tabrizu.ac.ir Abstract: Systems of nonlinear equations arise in a diverse range of sciences such as economics, engineering, chemistry, mechanics, medicine and robotics etc. For solving systems of nonlinear equa- tions, there are several methods such as Newton type method, Particle Swarm algorithm (PSO), Conjugate Direction method (CD) which each has their own strengths and weaknesses. The most widely used algorithms are Newton-type methods, though their convergence and effective perfor- mance can be highly sensitive to the initial guess of the solution supplied to the methods. This paper introduces a novel evolutionary algorithm called Cuckoo Optimization Algorithm, and some well-known problems are presented to demonstrate the efficiency and better performance of this new robust optimization algorithm. In most instances the solutions have been significantly improved which proves its capability to deal with difficult optimization problems. Keywords: Systems of Nonlinear Equations; Optimization; Cuckoo Optimization Algorithms; Evolutionary Algo- rithm. 1 Introduction Solving systems of nonlinear equations has always been important in science. Most of the scientific problems are related to the system of nonlinear equations. As you know, there are two types of system equations. The first type is linear and the second type is called nonlinear. There are several methods for the first type but there are few methods for the second type that the solution often comes with approximate. So far, several methods are presented for solving sys- tems of nonlinear equations. Existing methods have been tried to solve such problems in less time and with higher accuracy. The genetic algorithm is used in [1] and the particle swarm algorithm has been improved in [3] for solving systems of nonlinear equations. From mathematical methods we can point the Filled Func- tion methods [4]. In this paper, we introduce Cuckoo Optimization Algorithm (COA) for solving the systems of nonlinear equations. The results of cuckoo optimization algo- rithm are compared with other methods found in [1], [3] and [4] to illustrate the power and high efficiency of this algorithm. In sections 2, we will briefly overview the COA. In Section 3, how to apply cuckoo algorithm for solving systems of nonlinear equations will be explained. In Section 4, the obtained numerical results will be pre- sented as a comparison and finally in section 5, we have the conclusions and future works. * Corresponding Author, P. O. Box 51586-49456, F: (+98) 411 669-6012, T: (+98) 914 116-2612 191